On Pólya groups of some non-Galois number fields

Fuente: arXiv
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Main Author: Maarefparvar, Abbas
Format: Preprint
Published: 2024
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author Maarefparvar, Abbas
author_facet Maarefparvar, Abbas
contents We prove two conjectures proposed by Chabert and Halberstadt concerning Pólya groups of $S_4$-fields and $D_4$-fields. More generally, the latter will be proved for $D_n$-fields with $n \geq 4$ an even integer. Further, generalizing a result of Zantema, we also prove that the pre-Pólya group of a non-Galois field of a prime degree, e.g. an $A_5$-field, coincides with its Pólya group.
format Preprint
id arxiv_https___arxiv_org_abs_2408_09019
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On Pólya groups of some non-Galois number fields
Maarefparvar, Abbas
Number Theory
11R21, 11R29, 11R37
We prove two conjectures proposed by Chabert and Halberstadt concerning Pólya groups of $S_4$-fields and $D_4$-fields. More generally, the latter will be proved for $D_n$-fields with $n \geq 4$ an even integer. Further, generalizing a result of Zantema, we also prove that the pre-Pólya group of a non-Galois field of a prime degree, e.g. an $A_5$-field, coincides with its Pólya group.
title On Pólya groups of some non-Galois number fields
topic Number Theory
11R21, 11R29, 11R37
url https://arxiv.org/abs/2408.09019